Probability theory and decision theory
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This page about probability theory and decision theory will deal about Bayesian, that is, subjective probability, and its use in normative decision analysis.
 Probability theory [frequentist and subjective (Bayesian) approach] MarjaLeenalla sopivia kirjoja? Uncertainty 220230. Jouni
 Decision theory (utility, decision tree, utilitarian, egalitarian and other decision rules) Decision theory
Two approaches in probability
 Frequentist: Probability is the frequency distribution of outcomes, when a large number of similar events is repeated and obseverd, such tossing a coin, throwing a dice, or taking a blood test from a random sample of individuals in a population.
 Bayesian: When you are indifferent about choosing between A and B, your probability for U_{1} given A is E.
Basic rules in probability
The probability of A happening = p(A)
p(A)+p(not A)=1
p(A or B) = p(A)+p(B)p(A and B)
 If A and B are mutually exclusive: p(A)+p(B)
p(AB) = p(A given B) = p(A and B)/p(B)
p(A and B) = p(AB)p(B)
 If A and B not dependent (uncorrelated): p(A)p(B)
The probability of causation (POC)
POC = P(risk from the cause of interest)/P(risk due to all causes)
What is the POC for PM_{2.5} causing cardiovasular deaths in the EU?
What is the POC for vinylchloride causing angiosarcoma in liver?
POC(PM_{2.5} causing cardiovasular deaths in the EU):
350 000 deaths/a / 2 000 000 deaths/a = 0.175
"Internationally: Worldwide incidence also is low. Reports show angiosarcoma of the liver with an annual incidence of 2 cases per 10 million population, rising to 2.5 cases per 1000 population in workers exposed to vinyl chloride." [1]
POC(vinylchloride causing angiosarcoma in liver):
POC = (2.5*10^{3}  2*10^{7})/(2.5*10^{3}) = 0.99992
Bayes' rule
(en:Risk aversion en:Risk premium)
Decision rules:
 Utilitarian: max_{d}(E(∑(u_{d,i})))
 Egalitarian: max_{d}(E(min(u_{d,i})))
 Elitist: max_{d}(E(max(u_{d,i})))
u=utility, d=decision, i=individual
 Cost benetit analysis
 Cost effectiveness analysis